Question

f(x)= 8 - 0.5x^2 on the interval [-1,4]
What is the actual area under the curve using a right sum with 10 rectangles? (Solve using limits)

I'm not sure how to set this up.. any ideas?

Answer 1

\[\Delta x = \frac{ 5 }{ 10 } = \frac{ 1 }{ 2 }\]
\[x _{i} = -1+\frac{ i }{ 2 }\]
\[\frac{ 1 }{ 2 }\sum_{i=1}^{10} [8-0.5(-1+0.5 (\frac{ i }{ 2 })^2]\]
\[\frac{ 1 }{ 2 } \sum_{i=1}^{10} [8-0.5(-1+\frac{ 1 }{ 4 } (i^2)\]
\[\frac{ 1 }{ 2 } \sum_{i=1}^{10} [8-0.5(-1+\frac{ 1 }{ 4 } (\frac{ n(n+1)(2n+1) }{ 6 })\]
plug in 1-10 for i add together